Thermal techniques for the measurement of the mass flow rate of fluids generally fall into three catagories; viz: constant current, constant temperature, and boundary layer. With each technique, it has been the practice to employ two different sensors disposed in the fluid flow path and operating under different conditions from which the flow rate of the fluid may be calculated according to its cooling effect upon the sensors.
The constant current systems have been of either the thermistor type or the hot wire type. As is well known in the art, the prior art thermistor type is difficult to temperature compensate over a wide range of fluid temperature. At best, the temperature span is limited to approximately 50.degree. C. The principal problem in obtaining a broad temperature range is the inability to match the resistance/temperature characteristics of the thermistor pair. This problem is accentuated when one sensor is self heated and the other is not. Calibration, in any event, must always be empirical due to many sensor variables. Linearization may be obtained only with hand-tailored functions due also to variables from sensor to sensor and to transfer function dependency upon several of the sensor variables. Transfer functions are usually necessarily in the form of a second or third order exponential. Thus, standardization and interchangeability of transducers and their associated electronics are not practical.
Similar calibration and linearization limitations occur with the hot wire type of constant current system. Further, the high operating temperature required to obtain usable signal levels limits applications, sensor life, and sensor stability. Compensation over a broad temperature range is only slightly easier to obtain than with the thermistor type of constant current system.
Constant temperature techniques, of either the thermistor or hot wire type, suffer from the same general problems associated with the constant current systems. In addition, temperature compensation is limited by the difficulty of matching resistance/temperature characteristics of the compensation sensor to that of the flow sensor.
Applications using boundary layer techniques are distinctly limited due to the sensitivity to the differential temperature which exists between the transducer case and the fluid and to changes in the boundary layer characteristics due to pressure and temperature changes.
The present invention combines all the advantages of constant temperature operation with the accuracy and stability obtainable with thermistors due to their high signal level output and eliminates the shortcomings of thermistors in the prior art systems by making the transfer function virtually independent of variations in the thermistor's resistance/temperature curve. In point of fact, the technique described will work with any stable temperature variable device employed as a sensor. The temperature coefiecient may be positive or negative. Typical diverse devices are semi-conductors, metallic wires, and the like. The advantages of thermistors in most applications lies in their high sensitivity which minimizes the low level accuracy requirements imposed on the electronic signal conditioning apparatus.
The basic relationship for flow measurement using a sensor heated to a constant temperature (Ts) is: EQU P = (A + B m.sup.1/n) (Ts - Ta)
where:
P = power to sensor PA1 A = an empirically determined constant for zero flow (dependent on sensor size and specific fluid properties) PA1 B = an empirically determined constant for other then zero flow (also dependent on sensor size and specific fluid properties) PA1 m = mass flow rate = p V. PA1 n = an empirically determined constant dependent on physical size and shape of sensor, (typically 2.5 for thermistors used for mass flow rate measurements) PA1 Ts = Sensor operating temperature PA1 Ta = Fluid temperature
Fluid temperature dependence may be eliminated by operating two different sensors at two different constant temperatures and taking the difference in the power dissipations as follows: EQU P.sub.2 = (A + B m.sup.1/n) (Ts.sub.2 - Ta) EQU P.sub.1 = (A + B m.sup.1/n) (Ts.sub.1 - Ta) EQU P.sub.2 - P.sub.1 = (A + B m.sup.1/n) (Ts.sub.2 - Ts.sub.1) ##EQU1##
Since the sensors are operated at constant temperature, the resistance/temperature characteristics of the sensors do not appear in the transfer function. This is the derivation of "King's Law." For through treatment of King's Law, one may refer to: King, L. V. P., "On the Convection of Heat from Small Cylinders in a Stream of Fluid . . . ", Proceedings of the Royal Society, (London), Volume 214A, No. 14, 1914.
However, as a consequence of the previous noted problems, the accuracy which has heretofore been achieved by adhering to King's Law has been limited by the matching of the physical characteristics (mass, shape and surface area) of the two sensors and the placement of the sensors in the fluid stream such that they are exposed to the same fluid temperature and velocity simultaneously.